Ejemplo 11. Circunferencia tangente

[i]Sea P un punto de una recta y Q un punto que no pertenece a la recta. [/i][i]Dibuja la circunferencia que pasa por el punto Q y es tangente a la recta en el punto P.[/i][br][br]Comenzamos dibujando los objetos iniciales: una recta, un punto P en la recta que no sea ninguno de los puntos (A y B) utilizados para crearla y un punto Q que no pertenezca a la recta.[br][br][img 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encontrar la circunferencia pedida es necesario determinar su centro.[br][br]Como P y Q son puntos de la circunferencia, significa que el centro estará a la misma distancia de ellos. Por tanto, el centro estará en la mediatriz de los dos puntos o lo que es lo mismo, en la mediatriz del segmento PQ.[br][br]Seleccionamos la herramienta [b]Mediatriz[/b], pulsando a continuación sobre P y Q. Aparece la mediatriz, sin necesidad de haber dibujado previamente el segmento PQ.[br][br][img 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recta inicial es la tangente a la circunferencia en P, por lo que el radio trazado por P será perpendicular. [br]Esto supone que el centro se encontrará en la recta perpendicular a la recta por el punto P que trazamos utilizando la herramienta [b]Recta perpendicular[/b].[br][br][img 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punto de intersección de esta recta con la mediatriz dará el centro de la circunferencia que trazaremos utilizando la herramienta [b]Circunferencia (centro, punto)[/b] para obtener la circunferencia cuyo centro es C y un punto que puede ser P o Q.[br][br][img 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que la construcción está bien hecha moviendo los objetos iniciales. Por ejemplo, si movemos los puntos P o Q, la circunferencia seguirá cumpliendo las condiciones pedidas.

Information: Ejemplo 11. Circunferencia tangente